The EnKF is widely used and has shown to perform well for many applications in geosciences e.g. for the weather prediction [1]}, or for the radiation belts prediction [2]}. Radiation belts dynamics modeling consist in estimating quantitatively the fluxes of high energetic electrons and protons trapped in the Earth magnetic field using a typical advection-diffusion equation. This region spans from 1 Earth Radius up to 8, thus encompassing all typical satellites orbits, with which such particles can strongly interact and induced from minor to critical onboard anomalies. Compared with global prediction, radiation belts predictions are performed on a limited and non-periodic domain where the boundary imposes conditions to the dynamics of the electrons and protons. Indeed, on one side, the outer boundary condition is considered as the prime access for fresh materials, coming from the so-called magneto-tail, and is typically modeled as an imposed Dirichlet condition at this altitude (8 Earth radii) that can evolve as a function of solar activity (e.g. energy spectrum reshaping from time to time) [3]}. On the other side, close to the Earth, the atmosphere implies a necessary fixed Dirichlet condition too, as all radiation belts particles coming down there are absorbed (e.g. distribution always equal to 0). Finally, for low energy boundary we expect to rely on a Neumann condition to limit naturally any escape of particles or artificial source. Nonetheless, when performed on limited area models, atmospheric prediction also present such kind of boundaries.
